Using data-driven activities with ChemEd X Data to practice structure-property relationships in General Chemistry

General Chemistry covers a wide variety of structure-property relationships that rely upon electronic, atomic, crystal or molecular structure. Often these submicroscopic factors come into conflict: What has a higher boiling point, methanol or hexane? What atom has a larger radius, Li or Mg? O or Cl? A good strategy to address these “conflicting factors” is giving students experimental data at different points of the learning sequence and allow them to identify the patterns as well as identify the limit of predictability of such patterns.

“ChemEd X Data” is a web interface developed by the author (http://chemdata.r.umn.edu/, J. Chem. Educ, 2014, 91, 1501). This tool was designed for chemistry students to navigate, filter and graphically represent chemical and physical data. It can assist students at identifying trends in structure-property relationships, they can create controlled experiments to test a relationship as well as investigating how different molecular factors may affect a single macroscopic property. In particular, since the site offers unstructured but dynamically searchable data, it is designed to have students learn control of variable strategies (CVS) which are activities that require self-regulation and self-evaluation skills for its successful completion.

In this paper, students complete a common sequence of activities related to structure-property relationships using ChemEd X Data at different points of a General Chemistry semester. Student performance is analyzed through a common sequence of questions in different topics with the objective of understanding which activities require a higher cognitive skill, as well as identify the type of student background that correlates with success in the activities and in the course in general.

Introduction

There is a significant agreement among science faculty about the positive impact that the implementation of evidence-based pedagogical approaches and supportive learning environments have on student learning. Many science faculty have already adopted different forms of active learning in the class in order to increase student success, engagement, and retention. On the other hand, the content for science courses have not yet changed at the same rate. In other words, we changed “how to teach”, but we have not significantly changed “what to teach”. In order to revisit and improve what science students should learn, the President's Council of Advisors on Science and Technology (PCAST)1 and the National Research Council2 called instructors during the first two years of college to focus on deeper and transferable knowledge.

As a response to this call to action, the Next Generation for Science Standards (NGSS) has provided a very detailed framework and assessment tools for such implementation in K-12, which they can be easily applied to introductory science courses in college3.Following the standards provided by the NGSS, instructors should focus on core ideas, crosscutting concepts and scientific practices. Activities that include these three aspects aim at what it is has been called the three-dimensional learning4.

The aim of this paper is to shed some light on how instructors can successfully address several scientific practices during the first semester of a General Chemistry course in one of the most prevalent Chemistry’s core concepts, the “Atomic/Molecular Structure and Properties” or what is commonly known as structure-property relationships; in particular, how can ChemEd X Data website best help in some of the most open-ended or data-driven types of questions. The several student activities presented and analyzed here pertain to different topics and they are spread throughout a typical first semester of General Chemistry and should not require any major curriculum redesign.

The tool: ChemEd X Data website

ChemEd X Data5,6 (http://chemdata.r.umn.edu/chemedXdata/) was created to help students practice activities that address scientific practices, during introductory courses of chemistry. More specifically, ChemEd X Data was designed for chemistry students to navigate, filter and graphically represent chemical and physical data. The kind of activities that ChemEd X Data offers to students must be placed within the data-first or data-driven learning approach7,8. Even though data-first activities, data-driven activities and problem-based learning can sometimes be used interchangeably, there is some variability in terms of how data are made available to students. On one end, the data may be a table of already pre-selected values. In many of these cases the activity will be more focused on interpreting and manipulating the given data rather than navigating, plotting and choosing them. Therefore, it may exclude the possibility for open-endedness. On the other end of the spectrum, the student could be offered an unstructured spreadsheet of data or access to a database or a web portal such as Pubchem or Wikipedia9,10. In the latter case, the “open-endedness” may overwhelm students, or their performance may rely too much on their information literacy skills. The ChemEd X Data website tries to find a balance between the two extremes, where a large quantity of unstructured data is available while still trying to lower the technical barrier by making it easy to navigate, sort, rank and instantly plot different types of physical and chemical data. The three figures below show snapshots of ChemEd X Data most basic capabilities.

Figure 1 Flexible selection of compounds and their properties to discover trends in structure-property relationships: boiling and melting points, heat capacities, enthalpies of combustion, as a function of mass, shape, functional group…

Figure 2 Upon selecting a set of compounds, the user may click on the “View 3D!” button to visually explain the observed physical properties with molecular properties such as symmetry, charges and dipoles.

Figure 3 Navigate the periodic table to identify periodic trends or trends among inorganic compounds across a period or a group.

Implementation

The results presented in this paper were collected during the fall semester of a “General Chemistry 1” course at the University of Minnesota Rochester (UMR). The course was structured as a “flipped classroom”11. In this type of delivery, students were assigned to watch three or four videos (with a length of approximately 5 to 10 min each) and turn in the answers to a series of preclass questions. However, the days when students were asked questions related to creation of knowledge no videos nor any pre-class questions were assigned in regards to the knowledge they were going to create. The majority of students were in their sophomore year. UMR only offers two Bachelor of Sciences, both related to Health Sciences, and students must take at least one semester of introduction to Organic structure during their first year before enrolling in General Chemistry. This curriculum approach is called “organic first”12 and it is intended, in part, to improve their quantitative skills during their first year of college before enrolling in General Chemistry13. This approach also means that students are already very familiar with organic functional groups and organic molecular structures, which allowed the design of activities involving a wider range of organic compounds. Instructors at other institutions without an organic-first approach, should reformulate the activities that match students’ previous knowledge of molecular structure.

All the activities were delivered using the Moodle Learning Management System and students completed them individually either during class time or as homework outside of class. Some of the exercises required the use of ChemEd X Data but not all. Thanks to the laptop program, all students had a laptop during class time.

A common sequence of questions for several topics

Students completed a set of activities that pertain to three different topics with structure-property relationships, namely, periodic table trends, effect of size and charge on ionic bond, and factors affecting the boiling point of molecular solids. All these topics however, allowed us to build a common sequence of questions or progressions that students answered in those three different topics. The five-question sequence or progression can be simplified as:

1.Identify molecular factors

2.Connect structure and property by investigating data

3.Predict and apply relationship

4.Explain observations

5.Conflicting factors and identify limit of predictability

Students in the past had special difficulty in questions two and five. Number two is necessarily open ended and hard to implement in a regular class, and number five is somewhat counterintuitive to students, therefore they may deserve a deeper justification.

Investigating data: Control of Variable Strategy

This activity consists of being able to select experimental data to show evidence of a specific trend or law, or what is commonly known as designing a controlled experiment or control of variable strategies (CVS)14.See the work by Schwichow et al14 for an excellent overview on the pedagogical background in control of variable strategies. This activity represents one step further from what is commonly known as data-first problems8. In data-driven activities students are typically shown a specific arrangement of data. In the CVS case, however, students select the substances they want to represent, they must build a controlled experiment by keeping the rest of variables constant and varying the only one being tested. Therefore, there is not a unique valid answer and the problem becomes open-ended. As it has been previously described5, ChemEd X Data was specifically designed to practice this last kind of activity. Table 2 shows an example from students of a correct and incorrect selection of molecules to show evidence of the effect of linear/branching on the boiling point of organic molecules.

Table 1 An example of a correct (first row) and an incorrect (second row) selection could be when students are presented with the question “Select 4 compounds to show evidence of how the linear/branched chain may affect boiling points”.

Conflicting factors and limit of predictability

In General Chemistry, there are several curricular examples where there is typically more than one factor deciding an outcome. In introductory levels, the instructor may decide to either avoid examples with conflicting factors or have students learn to recognize the limit of predictability at a given level of theory. For example, students may learn that hydrogen bonds are stronger than London forces, but that is only true if other factors such as mass and shape are kept constant. Several works have been published on how to better understand and teach this topic15–18. If students are asked to predict whether methanol or hexane have the highest boiling point, they should first recognize that mass and intermolecular forces (IMF) are in conflict and that, at this level of theory, they do not have enough tools to predict an outcome. Alternatively, one can also reverse the question; if students are told that hexane has a higher boiling point than methanol they should be able to recognize that the mass is playing a larger role than the strength of intermolecular forces. This pedagogical route may be the recommended one. It is a good opportunity to address the scientific practices “Analyzing and interpreting data” as well as “Constructing Explanations and Engaging in Argument from Evidence”3 in introductory courses and it potentially eliminates any misconceptions or frustration that some students may feel when they realize that they are not being told “the total truth” or that chemistry has too many exceptions19,20. Table 1 lists the different cases in a typical “General Chemistry 1” semester where this conflict among factors is given.

Table 2 Topics typically present in a first semester of a college General Chemistry course where more than one structural or energetic factor may affect the property. The different factors may potentially be in conflict with each other.

Property to be predicted

Several factors that may come into conflict

Examples where content in introductory courses does not predict an outcome

Melting point or heat of fusion of molecular solids

Intermolecular forces, molecular shape and mass

Highest boiling point?Methanol vs Hexane

Periodic table trends: atom size and ionization energy of elements.

Nuclear charge, electronic shielding and orbital size.

What element has a larger radius among diagonal elements?(Li is bigger than Mg but O is smaller than Cl)

Ionic lattice energy of a crystalline solid

Cation and anion size and their ionic charge

What compound has a higher ionic lattice energy, KF or NaCl?

Electronic configuration of elements (ground state)

Hund’s rule and Aufbau principle

For chromium and molybdenum, the ground state is “s1 d5”, but for tungsten is “s2 d4” and carbon is “s2 p2”

VSEPR theory: molecular angle

Lone pairs and double bonds affecting the regular angle

Molecules where lone pairs and double bonds are present in the central atom: SO2, O3, NOCl

Heat capacity of molecules

Molecular mass, number of covalent bonds and intermolecular forces.

Highest heat capacity?propanol (more mass) vs butane (more bonds)

Miscibility of two liquid substances

Intermolecular forces and molecular shape

What is more soluble in water, butanol or dichloromethane?

Results and Discussion

The analysis of student performance in the “structure-property relationship” activities may be enriched if it is compared with students’ performance at the end of the course as well as in previous college courses.

As the figure below shows, three very distinct groups of students can be identified when representing “final course grade” vs “College GPA held at the beginning of the semester”. These three groups labeled as low performers (LP, black squares), intermediate performers (IP, green circles), and high performers (HP, red triangles) are the three clusters obtained using the k-means clustering analysis as it is implemented in the R package.All the points in the graph correlate fairly well to a linear behavior, with a Pearson’s product-moment correlation coefficient of 0.807. As it has been noted elsewhere21, albeit not being very informative in regards to students profile, the current students’ GPA is a good predictor for future course performances. These three groups of students, LP, IP and HP, will be used throughout the analysis of activities presented below.

Figure 4 The clustering of “students’ GPA at the beginning of the course” vs “course final grade” at the end of the course gives three groups of students labeled as Low Performers (LP, black squares), Intermediate Performers (IP, green circles), and High Performers (HP, red triangles).

The next three subsections present the graphical analysis of students answers to the sequence of the five questions in three General Chemistry topics: Periodic Table Trends, Ionic Lattice Energy of Crystalline Solids, and Boiling Point of Molecular Liquids. As it is indicated in the example questions, students had to use ChemEd X Data in some parts of the activity, but not all.

Periodic Table Trends

In this first activity, students investigate the periodic table trends, and answered a set of questions that follow the common progression indicated above. For space reasons the entire questions are not shown verbatim.

1)Identify Atomic factors: Identify Z, shielding and orbital size.Example: The charge of oxygen nucleus is ___, and the charge of carbon nucleus is___, the number of electrons of neutral oxygen is ____ …., oxygen valence electrons are in n=____...

2)Connect Structure and Property.Example: Use ChemEd X Data and choose a series of elements that show how the element radius is affected by the nuclear charge.

5)Identify limit of predictabilityExample: Which pair of elements present a conflict of factors that does not allow you to predict what element is bigger: Choose one or more. “Li vs O”, “O vs Mg”, “Li vs Mg”, “O vs Cl”

Figure 5 Sankey diagram showing the flow of students’ answers to a series of questions related to periodic table trends. The last column labeled “College performance” shows the fraction of students belonging to High Performers (HP), Intermediate Performers (IP), and Low Performers (LP) that answered correctly or incorrectly the last question on “identifying the limit of predictability”.

In the Sankey diagram of the figure above, each column represents a question in the activity. The horizontal stripes connecting the columns indicate the fraction of students who answered that specific question correctly (green) or incorrectly (red). For example, in the first question labeled as “Identify molecular factors”, the vertical line tells us that about 70% of students answered it correctly. Moving to the next question, labeled as “Connect structure and property”, that initial 70% of correct answers increases to 85%. One of the main advantages of this diagram is that it shows the flow of students’ answers among adjacent questions.

The last column in the figure above is not a question on this activity, it is a first attempt at understanding how performance in higher-level activities may relate to course performance and college GPA. In this case, because of the limitations of the Sankey diagram, we can only see what portion of students who obtained correct answers in the last question “Identify limit of predictability” belonged to each of the three college performance levels, LP, IP, and HP. The first thing that the results tell us is that students do not need to be High Performers (HP) to perform well in these specific higher-skill activities, but they need to be at least Intermediate Performers (IP).

Ionic Lattice Energy of Crystalline Solids

In this second activity related to how the charge and size of ions affect the energy of the ionic lattice, students answered a set of questions that follow the common progression indicated above. Again, for space reasons the entire questions are not shown verbatim.

1)Identify molecular factors: ion charge and trends in sizeExample: The size of Na is smaller/larger than the size of Cs. The charge of ion Na is smaller/larger/equal than ion Cs… (circle the correct option)

2)Connect structure and property: identify the role of size and charge in ionic lattice energy.Example: Based on your observations in ChemEd X Data, the smaller the ion the stronger/weaker the ionic lattice is (circle the correct option)

3)Predict and apply.Example: When comparing NaF and CsI, what compound will have a stronger ionic lattice?

4)Explain observations.Example: The energy of the ionic lattice for KF is larger than for LiF. Can this observation be explained by this theory?

Figure 6 Sankey diagram showing the flow of students’ answers to a series of questions related to the ionic bond. The last column labeled “College performance” shows the fraction of students belonging to High Performers (HP), Intermediate Performers (IP), and Low Performers (LP) that answered correctly or incorrectly the last question on “identifying the limit of predictability”.

Boiling Point of Molecular Liquids

The last of the activities, the boiling point of molecular liquids, is probably the topic where ChemEd X Data can be more useful. In the two cases above, periodic table trends and energy of the ionic lattice, there is a more limited dataset that students can explore, just few elements and few periods of columns. Therefore, it is not until this present topic when some of the exercises are truly open-ended and each student uses a completely different dataset to justify a trend or an exception. A sample of the sequence of questions is the following

1)Identify molecular factors: Connect functional groups and IMFExample: Identify each of the following functional groups with the intermolecular forces they present (H-bond, dipole-dipole or London forces)

2)Connect structure and property. Create relationship: building CVSExample: Use ChemEd X Data to select a set of compounds that show evidence of how mass affects the boiling point of molecular liquids.(see next section for a more detailed description of these activities)

3)Predict and apply relationship. Rank functional groups by boiling point.Example: Based on your investigations, rank the strength of intermolecular forces as they affect the boiling point of their compounds: H-bonds, London forces, dipole-dipole interactions.

4)Explain observations: mass or dipole: CHxCly vs CHxFyExample: The link below plots the boiling point of CH3Cl, CH2Cl2, CHCl3, CCl4.http://chemdata.r.umn.edu/chemedXdata/#stamp=1414679798226In this series, what is the property that controls over the others. Is it the dipole? That is, the most polar has the highest boiling point? Is it the mass? That is, the most massive has the highest boiling point?

5)Limit of predictability: Alkanes vs alcoholsExample: Alkanes only present London/dispersion forces, which are much weaker than hydrogen bonds. Does it mean that an alcohol because it presents hydrogen bond will always have a higher boiling point than an alkane? Investigate if a heavy alkane has a lower boiling point than a light alcohol. Explain and submit the URL with the selection of molecules.

Figure 7 Sankey diagram showing the flow of students’ answers to a series of questions related to the boiling point of molecular liquids. The last column labeled “College performance” shows the fraction of students belonging to High Performers (HP), Intermediate Performers (IP), and Low Performers (LP) that answered correctly or incorrectly the last question on “identifying the limit of predictability”.

Student performance in Controlled Variable Strategies (CVS)

Question number two in any of the sequences of questions above is the ideal opportunity when students can build knowledge by investigating trends and creating controlled experiments in truly open-ended data-driven exercises. This is particularly true when investigating the different factors affecting the boiling point of molecular liquids and it may justify a more detailed analysis.

ChemEd X Data offers a wide set of compounds and many ways to sort them. In this specific case, students were asked three different questions:

1.Select a set of molecules on ChemEd X Data in order to run a controlled experiment to investigate the effect of shape (linear or branched) on boiling points. Explain what you found out.

2.Select a set of molecules on ChemEd X Data in order to run a controlled experiment to investigate the effect of mass on boiling points. Explain what you found out.

3.Select a set of molecules on ChemEd X Data in order to run a controlled experiment to investigate what intermolecular forces are stronger (H-bonds, dipole-dipole or London forces) and therefore have a higher boiling point. Remember that in a controlled experiment the different molecules must keep shape and mass as constant as possible so that you are only assessing the effect of the intermolecular force.

As the table below shows, students perform very differently in CVS questions depending on what molecular property they are trying to investigate. When assessing the branch effect (first row), the majority of students are able to select a correct set of molecules in which the mass and IMF are kept constant while the level of branching of the alkyl chain is different and therefore being tested. While twice as many high performing students can answer that question correctly than low performing ones (81.3% vs 46.2%) there is no significant difference in the final course grade between students who can answer this question successfully and those who cannot (p = 0.12). On the other hand, when trying to build a controlled experiment to test the effect of intermolecular forces (last row), a much lower fraction of students in all three categories can correctly answer this question. The fraction of high performers who can do it well more than triples the fraction of low performers who can (31.3% vs 7.7%). And the final grade between successful students and unsuccessful ones is statistically significant (p = 0.016).

The results in this table seem to indicate that students are not necessarily challenged by the open-endedness of the question, nor navigating the website, but, rather, by the fact that some molecular and atomic factors are more difficult to identify, select and keep constant in a controlled experiment than others. In this case, when testing IMF, it is difficult to keep the mass approximately constant while changing the functional group.

Table 3 Results showing how students perform in three different exercises requiring Controlled Variable Strategies to examine the effect of branch/linear chains, mass and intermolecular forces (IMF) on the boiling point of molecular liquids. Students are divided in three groups as defined above HP: high performing; IP: Intermediate performing, and LP: low performing.

% of all students who answered correctly

% of HP students who answered correctly

% of IP students who answered correctly

% of LP students who answered correctly

Final % course grade average for students answering

Correctly/Incorrectly; p-value

Select molecules to assess branch effect

72.4%

81.3%

74.2%

46.2%

83.1/79.2; p = 0.12

Select molecules to assess mass effect

46.6%

50.0%

48.4%

30.8%

83.1/81.1; p = 0.37

Select molecules to assess IMF effect

27.6%

31.3%

32.3%

7.7%

85.8/80.6; p = 0.016

Conclusions

The conclusions can be highlighted in five main points.

1)A unified approach to structure-property relationships allows instructors to aim at specific skills of different cognitive levels throughout a General Chemistry semester.

2)The ChemEd X Data website facilitates the practice of some of these skills using data-first activities.

3)Sankey diagrams show us how students correct and incorrect answers flow through a sequence of questions.

4)The type of questions that students have the most trouble with are: “Control of Variable Strategy” (step 2) and “Identifying the limit of predictability” (step 5)

5)Students can better identify the limit of predictability when using ChemEd X Data.

6)CVS exercises are only possible with data-first activities. Student performance will depend on the type of molecular factor being tested.

Comments

I liked the use in gen chem of their prior knowledge from organic, making their memories recall the organic functional groups and build on the structure-property relationships they learned a year earlier.

You mentioned that UMR puts organic first to give time for students to strengthen their mathematical skills before gen chem. In the fall 2017 ConfChem, the Texas study and others noted the importance of “calculator-free” mental math skills in predicting gen chem success.

Is there any specific intervention done for your health science majors during first year to bolster computation and calculation skills needed in the sciences? If so, is there a non-calculator component to the intervention? Would the intervention be taught by math or science faculty? What courses with math content do they take first year to “get ready” for gen chem and the quantitative component of their higher-level health science courses?

For their majors, where in their sequence do most take physics?
-- rick nelson

I followed closely the ConfChem in the fall, as it is a problem that all undergraduate science instructors have to face. We've tried different things throughout the years. First we thought that just by offering a "college algebra" course during the first year students would be able to transfer the math knowledge onto physical sciences. That transfer didn't happen, so in order to help student transfer their knowledge, we designed a multidisciplinary first-year course taught by math, physics and chemistry faculty called "College Algebra with Physical Concepts". We made a website here (https://sites.google.com/r.umn.edu/mathatumr/home?authuser=0) and a publication (ref #13) that should be published soonish (I hope). The exercises that we show on the wesbite as example are mostly calculator-free, which, as you already know, makes students very nervous. We did observe some improvement in GenChem1 between those who took the interdisciplinary course and those who didn't, but the improvement was not significant and the measuring tool had room for improvement. So we are still thinking about how to best help our students gain those math skills. We're in the middle of yet another chemistry sequence rearrangement, along the same organic-first spirit, that progressively addresses the quantitative aspects.

They take physics typically in their sophomore or junior year, as it requires pre-calculus for Physics 1, and calculus for Physics 2.

Xavier. This program is truly awesome, and I love its back-and-forth inductive/deductive perspective! It makes great inroads into fostering the conceptual understanding that a student must acquire in order to become a competent problem-solver. Especially valuable is the training in selecting the appropriate data set for analysis.

It also looks like it has a steep learning-curve. How would you manage to have time to use this in Gen-Chem? Would students first learn how to use it in the earlier Orgo course?

Meanwhile, I’d really like to see the syllabus for your new year-long prep-course. And might I suggest a couple of ideas from The Chem-Math Project I presented in the ConfChem last fall?

In my own research I found many students matriculating with no physics and, if they had a quality physical-science course, it traditionally came four years previously and was probably mostly forgotten. This would suggest a one-semester physical-science course to fill in the gaps before or concurrent with gen-chem I (or even as part of an Intro-to-Chem course).

It would need to be taught by someone cognizant of the issues we have all been discussing, and its syllabus would by necessity have to be very carefully circumscribed, given limited time and the need for depth rather than breadth. Does your new course provide this kind of preparation?

The calculations used in this physical-science course (call them "Sci-Math" if you will, courtesy of Madeline Goodstein) would, of course, constitute the core of math skills the students would need in gen-chem (measurement, UA, sig-figs, percent, ratios & proportions, pre-algebra, etc.) I assume that your new course is constructed along these lines?

I should note that the mathematics part would not be taught exclusively by the math-department because then it would become "formal-math," as I have previously described. The instructor would have to know and understand the physical-science/chemistry applications. (However, it could be a mathematics instructor who is one of "us," like the two instructors with whom I was lucky to be able to collaborate.) Does your three-person team represent this model?

Have you had a 50- or 80-minute recitation devoted mainly to chem-math and problem-solving? In that venue, students could work with guidance to learn how to use PQtutor, ChemEd X Data, Chem-Review.net, Khan Academy, ALEKS, et al. It could be manned-up by a chemistry education grad-student, or PLTL students, or along the lines of the Colorado Learning Assistant program.

1) The ChemEd X Data website does have a learning curve. Prior to any of the student data that I'm showing here our students had already used the website for an activity assigned as homework. Also we are planning on having during a first-semester chemistry some lab time for data representation and data interpretation, so it should work well for a dry lab.

2) I agree about the need for a physical science pre-knowledge, unfortunately, our college algebra course is only one semester and while we spend some time on SI Units and unit conversion, we don't go too deep into the physical meaning.

3) That's a good point. Yes and no. Our College Algebra course focuses on the mechanics of math with a the science context, but the physical and chemical context is not the main learning objective. In other words when we designed the course we had to choose if it was structured according to physical concepts or according to the typical math structure. So we decided to make it a math course (transfer and course descriptor issues...) and it is structured in the sequence of the math course (arithmetics, function representation, polynomial, rational and exponential functions...). We work quite closely, actually we are all in the same department, and the math faculty are "one of us", but at the end of the day, the structure of topics dictates the flavor of the entire course.

4) Not in the math course. Of course in GenChem we spend a long time on problem solving. More specifically, we do context-rich "open-ended" problems like the ones described by Overton et al http://pubs.rsc.org/en/Content/ArticleLanding/2013/RP/C3RP00028A#!divAbstract This is somewhat tangential to your question, but I have found the open-ended problems quite interesting in terms of helping students gain a physical sense of numerical magnitudes. In these problems (also called Fermi problems) students need to make educated guesses and find a reasonable solutions.

Although this 'web interface' is a commendable achievement, one should be aware of the formal usage of terms and units. For instance, in the inorganic display, the units of mass and atomic radius are not indicated in the sample table. The mass must be specified with a unit, specifically 'mass/u' and the atomic radius must be specified with its unit, specifically 'atomic radius/*' in which * might be nm, or pm, or even 10-10 m, but not angstrom unit of which the use is deprecated according to the International System of Symbols, Units and Notation. How can we expect the students to learn to use proper units and notation if we are ourselves remiss in this regard?

In the above text, '-10' was entered as a superscript, but does not appear to be presented in this manner.